An off-axis circle criterion for feedback systems containing a single time-invariant nonlinearity

Describes a graphical evaluation of the robust stability for control systems in a frequency domain in which Popov´s criterion was expressed in an explicit form. The control system described herein is a feedback system containing a single time-invariant nonlinearity in the forward path. By applying the small gain theorem that concerns L₂ gain in regard to a nonlinear subsystem with a free parameter. A robust stability condition for control systems with a sector nonlinearity is presented. Using this concept, we show a representation of an off-axis circle criterion on a Nyquist diagram, and propose an evaluation method of the stability from the relative position with the vector locus of the open loop frequency response characteristic. In the paper, the relationship between the robust stability condition and the usual graphical method of Popov´s criterion is discussed